On Pickands coordinates in arbitrary dimensions

We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an 1 -symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

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“…where the function A is the so-called Pickands dependence function; see [15], [26, p. 312], and [33]. That is, A : {x…”

Section: Extremal Behavior Of Archimedean Copulasmentioning

confidence: 99%

Extremal behavior of Archimedean copulas

Larsson

Nešlehová

2011

Adv. Appl. Probab.

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“…For the bivariate case, the extreme value copula may be written as In Eq. (19), A denotes the Pickands dependence function (Pickands 1981;Falk and Reiss 2005) that is convex as…”

Section: Copula Families and Parameter Estimationmentioning

confidence: 99%

Copula–entropy theory for multivariate stochastic modeling in water engineering

Singh

Zhang

2018

Geosci. Lett.

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The copula-entropy theory combines the entropy theory and the copula theory. The entropy theory has been extensively applied to derive the most probable univariate distribution subject to specified constraints by applying the principle of maximum entropy. With the flexibility to model nonlinear dependence structure, parametric copulas (e.g., Archimedean, extreme value, meta-elliptical, etc.) have been applied to multivariate modeling in water engineering. This study evaluates the copula-entropy theory using a sample dataset with known population information and a flood dataset from the experimental watershed at the Walnut Gulch, Arizona. The study finds the following: (1) both univariate and joint distributions can be derived using the entropy theory. (2) The parametric copula fits the true copula better using empirical marginals than using fitted parametric/entropy-based marginals. This suggests that marginals and copula may be identified separately in which the copula is investigated with empirical marginals. (3) For a given set of constraints, the most entropic canonical copula (MECC) is unique and independent of the marginals. This allows the universal solution for the proposed analysis. (4) The MECC successfully models the joint distribution of bivariate random variables. (5) Using the "AND" case return period analysis as an example, the derived MECC captures the change of return period resulting from different marginals.

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“…A generalization of Pickands' dependence function to the multivariate case is shown in Falk and Reiss (2005). Since A can be estimated via empirical data (Genest and Segers, 2009), then it may be used to check the statistical adequacy of different models.…”

Section: Mev Copulas: An Overviewmentioning

confidence: 99%

“…In fact, the use of measures of association φ (i) C 's for ruling the fits (instead of full dependence structures, as in the 1-MEV approach) may discard some important details: roughly speaking, a few "moments" of a distribution may not provide the same information as of the distribution itself. As an obvious alternative, we might suggest to use in the fits some multivariate equivalents of the bivariate Pickands' dependence functions (Falk and Reiss, 2005), but the research in this area is still in its infancy, and it is not yet clear how to proceed.…”

Section: The Cluster Approachmentioning

confidence: 99%

Estimating strategies for multiparameter Multivariate Extreme Value copulas

Salvadori

Michele

2011

Hydrol. Earth Syst. Sci.

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Abstract. Multivariate Extreme Value models are a fundamental tool in order to assess potentially dangerous events. Exploiting recent theoretical developments in the theory of Copulas, new multiparameter models can be easily constructed. In this paper we suggest several strategies in order to estimate the parameters of the selected copula, according to different criteria: these may use a single station approach, or a cluster strategy, or exploit all the pair-wise relationships between the available gauge stations. An application to flood data is also illustrated and discussed.

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On Pickands coordinates in arbitrary dimensions

Cited by 35 publications

References 33 publications

Extremal behavior of Archimedean copulas

Extremal behavior of Archimedean copulas

Copula–entropy theory for multivariate stochastic modeling in water engineering

Estimating strategies for multiparameter Multivariate Extreme Value copulas

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